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Tiếng Việt
Date Published: 30/10/2025
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DOI: 10.54607/hcmue.js.22.10.4940(2025)
Issue
Tập 22, Số 10(2025)
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Articles
How to Cite
Pham, P. H., Mai, T. T. N., & Ta, T. T. M. (2025). SPACE-TIME FINITE ELEMENT METHOD FOR SOLVING REACTION-DIFFUSION EQUATIONS. Ho Chi Minh City University of Education Journal of Science, 22(10), 1874-1886. https://doi.org/10.54607/hcmue.js.22.10.4940(2025)

SPACE-TIME FINITE ELEMENT METHOD FOR SOLVING REACTION-DIFFUSION EQUATIONS

Pham Phi Hung1, Mai Thi Tuyet Nhung1, Ta Thi Thanh Mai1,
1 Hanoi University of Science and Technology

Main Article Content

Abstract

In this paper, we present a space-time finite element method for the approximate solution of reaction–diffusion equations. Unlike traditional numerical approaches that discretize the temporal and spatial domains separately, the proposed method discretizes the space-time domain Q = Ω × (0, T) simultaneously on a unified mesh structure. This unified treatment reduces computational cost and enhances the accuracy of the approximate solution. The method reformulates the original problem into a variational (weak) form, and the well-posedness of the weak formulation is established via the Banach–Nečas–Babuška theorem, ensuring the existence and uniqueness of the solution. A priori error estimates demonstrate that the method achieves optimal convergence rates in the corresponding function spaces. The effectiveness and accuracy of the approach are further validated through numerical experiments conducted using the open-source software FreeFEM++.

Keywords

a priori error estimates, FreeFEM , reaction-diffusion equations, Space-time finite element method

Article Details

References

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